Extension of multidimensional microscopy to ultra-sensitive applications with maximum-likelihood analysis

Multidimensional fluorescence microscopy is finding service in forefront biological studies that require separation of images from different fluorophores. For example, commercial microscopes are available with multi-band analog detectors and user-friendly software for “linear unmixing” of species with overlapping emission spectra. To extend such techniques to ultrasensitive and single-molecule applications, we have developed a custom-built microscope, which incorporates two tunable-wavelength picosecond dye lasers for pulse-interleaved laser excitation, angle-tuned reflection of the laser beams from narrow-band Raman notch filters to introduce epi-illumination and provide strong rejection of scattered laser wavelengths, diffraction-limited confocal imaging with 3-dimensional piezo-scanning, an adjustable prism spectrometer for high-throughput resolution of collected fluorescence into 4 spectral bands, and a 4-channel highquantum efficiency avalanche diode for sub-nanosecond-resolved single-photon detection. Custom software enables multi-band fluorescence correlation spectroscopy and identification of photon bursts for single-molecule detection. For unmixing of spectrally-overlapping signatures for ultrasensitive molecular imaging applications, we find that maximumlikelihood analysis can out-perform least-squares-based linear unmixing in the regime of low photon numbers per spectral/temporal channel. Also, the likelihood surface provides the confidence of the parameter estimates and the covariance of the species contributions. Monte Carlo simulations show that bias in the results of the analysis, which stems from the constraint that photon numbers should be positive, becomes more pronounced at low signal levels, for both maximum-likelihood and least-squares based unmixing.